Backtracking Direct, Indirect and Total Effects

Jose M. Peña

stat.MEOct 20, 2026

Backtracking Direct, Indirect and Total Effects

Authors: Jose M. Peña

Organizations: STIMA, IDA, LiU

Abstract

Natural direct and indirect effects are defined through cross-world interventional counterfactuals. We propose an alternative construction based on backtracking counterfactuals. Rather than intervening on the treatment or mediator, we use a backtracking conditional distribution to construct an alternative exogenous state satisfying a desired treatment-mediator constraint. This yields the backtracking direct and indirect effects, and also the backtracking total effect. Likewise, we adapt the population intervention effects.

Causal Effect Estimation

Causal effect estimation measures how outcomes would change under interventions, using experiments or observational data and explicit assumptions.

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Conformal Individual Treatment Effect Estimation under Networked Interference

Matteo Zecchin, Osvaldo Simeone

Communication Systems Department, EURECOM, Sophia Antipolis, France · Institute for Intelligent Networked Systems (INSI), Northeastern University London, London, UK

Weighted Conformal Prediction Causal Effect Estimation Counterfactual Prediction Conformal Prediction Causal Inference Individualized Treatment Effect Estimation

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Conformal counterfactual prediction constructs prediction sets with finite-sample coverage guarantees for counterfactual outcomes and individual treatment effects under the no-interference assumption. In this work, we relax this assumption by allowing each unit's potential outcomes to depend on other units' treatments and covariates. In this setting, propensity-score reweighting does not restore weighted exchangeability, and existing methods may fail to achieve valid coverage. To address this issue, we develop interference-adjusted weighted conformal prediction that accounts for interference by constructing an observable upper bound on the ideal and unobserved conformal

p

-value under the target intervention. The resulting prediction sets provide finite-sample marginal coverage guarantees for counterfactual outcomes and individual treatment effects in both transductive and inductive settings. We also derive a sharper construction when intervention-induced changes in nonconformity scores are bounded. Numerical experiments show that our methods preserve nominal coverage, whereas existing methods may not.

Abstract

Causal Effect Estimation

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